This proposal is for a renewal of our grant in which we developed the theory for a Bayesian estimator for censored survival data and related problems. We wish to continue our work in this area both for Bayesian statistical problems and others of which we have become aware when the data available is randomly right censored. We propose to develop various two sample and k-sample tests based on estimated mean survival time, median survival time and related linear combinations of censored observations. This, we hope to do by building upon our asymptotic theory already developed under our current grant. In addition to this, we shall investigate various empirical Bayes problems for censored data extending our work in reference (46) under the current grant. Another area of investigation will be the estimation of densities, survival functions, and hazard rates for censored survival data. Some preliminary work has already been done in this area under the current grant in references (7) and (11). Along with this, we shall address ourselves to a host of related problems in censored survival analysis, including power consideration of the tests derived, small sample properties of the tests and estimates, the incorporation of patient covariate information in survival using a proposed extension of the Cox model, and other possible related problems as they arise.